881421. Kth smallest element
Here is a detailed Markdown blog post for the problem "Kth smallest element" on GeeksforGeeks:
Kth smallest element
Summary
Given an array of integers, find the kth smallest element in it. This problem involves using a priority queue or heap data structure to solve.
Detailed Explanation
The idea is to use a min-heap to store the elements from the array and then extract the root k times to get the kth smallest element. We start by inserting all elements of the array into the min-heap. Then, we extract the minimum (smallest) element from the heap k times. This will give us the kth smallest element.
Here is a step-by-step breakdown of the solution:
- Initialize an empty priority queue or min-heap.
- Insert all elements of the array into the min-heap. Since it's a min-heap, this will ensure that the smallest element is always at the top.
- Extract the minimum (smallest) element from the heap k times. This can be done using a method like
extractMin()in a priority queue or a heap data structure. - The kth extracted element will be the kth smallest element in the array.
Time complexity: O(k log n), where n is the size of the array and k is the value of k (the kth smallest element we are looking for). This is because each extraction from the min-heap takes logarithmic time, and we do this k times.
Space complexity: O(n), as we need to store all elements in the min-heap.
Optimized Solutions
Java
import java.util.PriorityQueue;
public class KthSmallest {
public static int findKthSmallest(int[] arr, int k) {
PriorityQueue<Integer> pq = new PriorityQueue<>();
for (int num : arr) {
pq.offer(num);
}
for (int i = 0; i < k - 1; i++) {
pq.poll();
}
return pq.peek();
}
}